Giải bất phương trình lg

L

lovelycat_handoi95

[TEX]BPT \Leftrightarrow \frac{3cosx+cos3x}{4}cos3x-\frac{3sinx-sin3x}{4}sin3x \leq \frac{5}{8} \\\Leftrightarrow 3(cos3xcosx-sin3xsinx)+cos^23x+sin^23x \leq \frac{5}{2}\\ \Leftrightarrow 3cos4x+1 \leq \frac{5}{2}\\ \Leftrightarrow cos4x \leq \frac{1}{2} \\ \Leftrightarrow \frac{\pi}{12}+\frac{k\pi}{2} \leq \frac{5\pi}{12}+\frac{k\pi}{2}(k \in Z)[/TEX]
 
H

heartrock_159

Phương trình tương đương:

[TEX]\frac{1}{4}.(cos3x+3cosx).cos3x - \frac{1}{4}.(3sinx-sin3x}.sin3x \leq \frac{5}{8}[/TEX]

[TEX]\Leftrightarrow \frac{1}{4}(cos^2 3x + sin^2 3x) + \frac{3}{4}.cos3x.cosx - \frac{3}{4}.sinx.sin3x \leq \frac{5}{8}[/TEX]

[TEX]\Leftrightarrow 2cos4x \leq 1[/TEX]

Dễ rồi nhé :)
 
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